Material-stiffening suppresses elastic fingering and fringe instabilities

When a confined elastic layer is under tension, undulations can occur at its exposed surfaces, giving the fingering or fringe instability. These instabilities are of great concern in the design of robust adhesives, since they not only initiate severe local deformations in adhesive layers but also cause non-monotonic overall stress vs. stretch relations of the layers. Here, we show that the strain stiffening of soft elastic materials can significantly delay and even suppress the fringe and fingering instabilities, and give monotonic stress vs. stretch relations. Instability development requires local large deformation, which can be inhibited by material-stiffening. We provide a quantitative phase diagram to summarize the stiffening's effects on the instabilities and stress vs. stretch relations in confined elastic layers. We further use numerical simulations and experiments to validate our findings.